The present invention relates to a control system for a plant, which uses a self-tuning regulator, and also relates to an air-fuel ratio control system for controlling, to a target value, an air-fuel ratio of an air-fuel mixture to be supplied to an internal combustion engine.
An example of a control system for a plant, which uses a self-tuning regulator is described in Japanese Patent Laid-open No. 11-73206 . FIG. 15 is a block diagram showing a general configuration of a control system using a self-tuning regulator 104 as shown in this publication. The self-tuning regulator 104 includes a parameter adjusting mechanism 105 and an inverse transfer function controller 106. The parameter adjusting mechanism 105 identifies model parameters (which will be hereinafter referred to also as “self-tuning parameters”) of a controlled object model obtained by modeling a controlled object (an engine system). The inverse transfer function controller 106 calculates a self-tuning correction coefficient KSTR by an inverse transfer function of a transfer function of the controlled object model by using the model parameters identified by the parameter adjusting mechanism 105. An air-fuel ratio detected by an air-fuel ratio sensor 17 is converted into a detected equivalent ratio KACT by a converting section 103, and the detected equivalent ratio KACT is supplied to the self-tuning regulator 104.
A target value calculating section 102 calculates a target air-fuel ratio coefficient KCMD (target equivalent ratio) corresponding to a target air-fuel ratio, and inputs the target air-fuel ratio coefficient KCMD into a fuel amount calculating section 101 and the inverse transfer function controller 106. The parameter adjusting mechanism 105 identifies the model parameters according to the detected equivalent ratio KACT and the self-tuning correction coefficient KSTR. The inverse transfer function controller 106 calculates a present value of the self-tuning correction coefficient KSTR according to the target equivalent ratio KCMD, the detected equivalent ratio KACT, and past values of the self-tuning correction coefficient KSTR. The self-tuning correction coefficient KSTR and the target equivalent ratio KCMD are input to the fuel amount calculating section 101. The fuel amount calculating section 101 calculates a fuel amount TOUT, that is, an amount of fuel to be supplied to an internal combustion engine (which will be hereinafter referred to also as “engine”) 1, using the target air-fuel ratio coefficient KCMD, the self-tuning correction coefficient KSTR, and other correction coefficients.
More specifically, the engine system as a controlled object is modeled into a controlled object model (DARX model (delayed autoregressive model with exogenous input)) defined by Eq. (1) shown below:KACT(k)=b0×KSTR(k−2)+r1×KSTR(k−3) +r2×KSTR(k−4)+r3×KSTR(k−5)+s0×KACT(k−2)  (1)where b0, r1, r2, r3, and s0 are the model parameters identified by the parameter adjusting mechanism 105. When a model parameter vector θ (k) having the model parameters as elements is defined by Eq. (2), shown below, the model parameter vector θ (k) is calculated from Eq. (3) shown below:θ(k)T=[b0, r1, r2, r3, s0]  (2)θ(k)=EPSθ(k−1)+KP(k)ide(k)  (3)where KP(k) is a gain coefficient vector defined by Eq. (4) shown below, and ide(k) is an identification error defined by Eq. (5), shown below. Further, EPS is a forgetting coefficient vector defined by Eq. (6), shown below. In Eq. (6), ε is a forgetting coefficient which is set to a value between “0” and “1”:
                              KP          ⁡                      (            k            )                          =                              P            ⁢                                                  ⁢                          ζ              ⁡                              (                k                )                                                          1            +                                                            ζ                  T                                ⁡                                  (                  k                  )                                            ⁢              P              ⁢                                                          ⁢                              ζ                ⁡                                  (                  k                  )                                                                                        (        4        )            ide(k)=KACT(k)−θ(k−1)T ζ(k)  (5)EPS=[1, ε, ε, ε, ε]  (6)
In Eq. (4), P is a square matrix wherein the diagonal elements are constants and all the other elements are “0”. In Eqs. (4) and (5), ζ (k) is a vector defined by Eq. (7), shown below, and having a control output (KACT) and control inputs (KSTR) as elements.ζ(k)T=[KSTR(k−2), KSTR(k−3), KSTR(k−4), KSTR(k−5), KACT(k−2)]  (7)
Further, the inverse transfer function controller 106 determines the control input KSTR(k) so that Eq. (8), shown below, holds:KCMD(k)=KACT(k+2)  (8)
By applying Eq. (1) to Eq. (8), the right side of Eq. (8) becomes:KACT(k+2)=b0×KSTR(k)+r1×KSTR(k−1) +r2×KSTR(k−2)+r3×KSTR(k−3)+s0×KACT(k)  (8a)
Accordingly, the following equation (9), shown below is obtained from Eqs. (8) and (8a). The control input KSTR(k) is calculated from Eq. (9):KSTR(k)=(1/b0)[KCMD(k)−r1×KSTR(k−1) −r2×KSTR(k−2)−r3×KSTR(k−3)−s0×KACT(k)]  (9)
That is, the inverse transfer function controller 106 calculates the control input KSTR(k) so that a deviation e(k) between a future equivalent ratio KACT(k+2) which will be detected two control cycles later, and the present value KCMD(k) of the target equivalent ratio, becomes “0”. The deviation e(k) is defined by Eq. (10), shown below:e(k)=KACT(k+2)−KCMD(k)  (10)
The characteristic of the controlled object model defined by Eq. (1) does not completely coincide with the characteristic of the actual controlled object, but includes a modeling error (the difference between the characteristic of the controlled object model and the characteristic of the actual controlled object). Further, the parameter adjusting mechanism 105 adopts a fixed gain algorithm. Accordingly, when the target equivalent ratio KCMD changes stepwise as shown in FIG. 16, the detected equivalent ratio KACT is influenced by the identification behavior of the model parameters due to the modeling error and the fixed gain algorithm, which sometimes results in an overshoot of the detected equivalent ratio KACT with respect to the target equivalent ratio KCMD.
Such overshoot causes a reduction in the purification rate of a catalyst provided in an exhaust system of the engine. This results in a deterioration of exhaust characteristics. Furthermore, depending on engine operating conditions, there is a possibility of causing an engine output surge wherein the engine driving force fluctuates.